Get connected databases info

The entry point is a project component

com.intellij.database.psi.DbPsiFacade

The database model API (tables, columns, etc.) is in the package

com.intellij.database.model

 So you do something like this:

// iterate through all data sources (project and global)
for (DbDataSource dataSource : DbPsiFacade.getInstance(project).getDataSources()) {

  // dataSource.getModel().traverser() will list all the objects

  // com.intellij.database.util.DasUtil is a convenience class for the same task:
  // e.g. iterate through all tables
  for (DasTable table : DasUtil.getTables(datasource)) {
    
  }
}